Exceptional points and cusp singularities in relativistic stellar oscillations with causal bulk relaxation

Causal relativistic hydrodynamics introduces relaxation degrees of freedom that elevate a quadratic oscillation problem to a cubic non-Hermitian spectral pencil. We study its exceptional-point (EP2) curves and an $A_3$ cusp, and construct an exactly solvable radiating wave--relaxation problem with a Pöschl--Teller potential and an Israel--Stewart channel. Using hyperboloidal coordinates, outgoing Siegert conditions become endpoint conditions. For the aligned transport profile and away from discrete resonant couplings, we prove that the complete quasinormal point spectrum decomposes into a tower of sector cubics, with radiative damping rates determined by the boundary-value problem. The resulting EP2 and cusp geometry is therefore realized by genuine quasinormal eigenvalues. Multiprecision bordered-Newton calculations certify the degeneracies and their square-root and cubic-root splitting laws. Under a controlled parity-preserving deformation of the viscosity profile, the fundamental EP2 survives over a finite parameter window before annihilating with a partner and moving into complexified parameters; the cusp also persists. For dense matter, we derive a criterion independent of the relaxation time: $(v_{\rm FR}/v_β)^2 \ge 1+Θ(γ)$, where $Θ(γ)$ is the minimum coupling ratio along the EP2 locus. For weakly radiating compressive modes, $Θ\simeq 8$, requiring $v_{\rm FR}\gtrsim 3v_β$. Internally consistent nucleonic Urca matter misses this threshold by more than two orders of magnitude. Exotic-matter comparisons are indicative benchmarks rather than same-equation-of-state exclusions. The radiating model is not a relativistic TOV-star perturbation; establishing the mechanism in a realistic star remains open.

Source: arXiv:2610.33089v1 - http://arxiv.org/abs/2610.33089v1 PDF: https://arxiv.org/pdf/2610.33089v1 Original Link: http://arxiv.org/abs/2610.33089v1